ÌâÄ¿ÄÚÈÝ
ÈçͼËùʾ£¬Æ¤´ø´«¶¯×°ÖÃÓëˮƽÃæ¼Ð½ÇΪ30¡ã£¬Âְ뾶R= m£¬Á½ÂÖÖáÐÄÏà¾àL=3£®75m£¬A¡¢B·Ö±ðʹ´«ËÍ´øÓëÁ½ÂÖµÄÇе㣬ÂÖÔµÓë´«ËÍ´øÖ®¼ä²»´ò»¬¡£Ò»¸öÖÊÁ¿Îª0£®1kgµÄСÎï¿éÓë´«ËÍ´ø¼äµÄ¶¯Ä¦²ÁÒòÊýΪ¦Ì= ¡£gÈ¡10m/s2¡£
£¨1£©µ±´«ËÍ´øÑØÄæʱÕë·½ÏòÒÔv1=3m/sµÄËÙ¶ÈÔÈËÙÔ˶¯Ê±£¬½«Ð¡Îï¿éÎÞ³õËٵطÅÔÚAµãºó£¬ËüÔ˶¯ÖÁBµãÔ¼Ðè¶à³¤Ê±¼ä£¿
£¨2£©Ð¡Îï¿éÏà¶ÔÓÚ´«ËÍ´øÔ˶¯Ê±£¬»áÔÚ´«ËÍ´øÉÏÁôϺۼ£¡£µ±´«ËÍ´øÑØÄæʱÕë·½ÏòÔÈËÙÔ˶¯Ê±£¬Ð¡Îï¿éÎÞ³õËٵطÅÔÚAµã£¬Ô˶¯ÖÁBµã·É³ö¡£ÒªÏëʹСÎï¿éÔÚ´«ËÍ´øÉÏÁôϵĺۼ£×£¬´«ËÍ´øÔÈËÙÔ˶¯µÄËÙ¶Èv2ÖÁÉÙ¶à´ó£¿
½â´ð£º £¨1£©µ±Ð¡Îï¿éËÙ¶ÈСÓÚ3m/sʱ£¬Ð¡Îï¿éÊܵ½ÊúÖ±ÏòÏ¡¢´¹Ö±´«ËÍ´øÏòÉϵÄÖ§³ÖÁ¦ºÍÑØ´«ËÍ´øбÏòϵÄĦ²ÁÁ¦×÷Óã¬×öÔȼÓËÙÖ±ÏßÔ˶¯£¬Éè¼ÓËÙ¶ÈΪa1£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉ
mgsin30¡ã + ¦Ìmgcos30¡ã=ma1 ¢Ù
½âµÃ a1 = 7£®5m/s2
µ±Ð¡Îï¿éËٶȵÈÓÚ3m/sʱ£¬ÉèСÎï¿é¶ÔµØλÒÆΪL1£¬ÓÃʱΪt1£¬¸ù¾ÝÔȼÓËÙÖ±ÏßÔ˶¯¹æÂÉ
t1 = ¢Ú
L1 = ¢Û
½âµÃ t1 = 0£®4s L1 = 0£®6m
ÓÉÓÚL1£¼L ÇҦ̣¼tan30¡ã£¬µ±Ð¡Îï¿éËٶȴóÓÚ3m/sʱ£¬Ð¡Îï¿é½«¼ÌÐø×öÔȼÓËÙÖ±ÏßÔ˶¯ÖÁBµã£¬Éè¼ÓËÙ¶ÈΪa2£¬ÓÃʱΪt2£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂɺÍÔȼÓËÙÖ±ÏßÔ˶¯¹æÂÉ
mgsin30¡ã£¦Ìmgcos30¡ã=ma2 ¢Ü
½âµÃ a2 = 2£®5m/s2
L£L1 = v1t2 + a2t22 ¢Ý
½âµÃ t2 = 0£®8s
¹ÊСÎï¿éÓɽûÖ¹³ö·¢´ÓAµ½BËùÓÃʱ¼äΪ t = t1 + t2 = 1£®2s
£¨2£©×÷v¡ªtͼ·ÖÎöÖª£º´«ËÍ´øÔÈËÙÔ˶¯µÄËÙ¶ÈÔ½´ó£¬Ð¡Îï¿é´ÓAµãµ½BµãÓÃʱԽ¶Ì£¬µ±´«ËÍ´øËٶȵÈÓÚijһֵv¡ä ʱ£¬Ð¡Îï¿é½«´ÓAµãÒ»Ö±ÒÔ¼ÓËÙ¶Èa1×öÔȼÓËÙÖ±ÏßÔ˶¯µ½Bµã£¬ËùÓÃʱ¼ä×î¶Ì£¬¼´
L = a1tmin2 ¢Þ
½âµÃtmin = 1s
v¡ä =a1tmin =7£®5m/s
´ËʱСÎï¿éºÍ´«ËÍ´øÖ®¼äµÄÏà¶Ô·³ÌΪ ¡÷S = v¡ä t£L = 3£®75m
´«ËÍ´øµÄËٶȼÌÐøÔö´ó£¬Ð¡Îï¿é´ÓAµ½BµÄʱ¼ä±£³Ö²»±ä£¬¶øСÎï¿éºÍ´«ËÍ´øÖ®¼äµÄÏà¶Ô·³Ì¼ÌÐøÔö´ó£¬Ð¡Îï¿éÔÚ´«ËÍ´øÉÏÁôϵĺۼ£Ò²¼ÌÐøÔö´ó£»µ±ºÛ¼£³¤¶ÈµÈÓÚ´«ËÍ´øÖܳ¤Ê±£¬ºÛ¼£Îª×Smax£¬Éè´Ëʱ´«ËÍ´øËÙ¶ÈΪv2£¬Ôò
Smax = 2L + 2¦ÐR ¢ß
Smax = v2t£L ¢à
ÁªÁ¢¢Þ¢ß¢à½âµÃ v2 = 12£®25m/s
½âÎö:
ÂÔ